TSTP Solution File: KLE011+1 by Prover9---1109a

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Prover9---1109a
% Problem  : KLE011+1 : TPTP v6.0.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire_rel --proof tptp --output_axiom_names on --mode casc -t %d %s

% Computer : n160.star.cs.uiowa.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory   : 32286.75MB
% OS       : Linux 2.6.32-431.11.2.el6.x86_64
% CPULimit : 300s
% DateTime : Mon Jun  9 23:49:02 EDT 2014

% Result   : Theorem 83.25s
% Output   : Refutation 83.25s
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : KLE011+1 : TPTP v6.0.0. Released v4.0.0.
% % Command  : vampire_rel --proof tptp --output_axiom_names on --mode casc -t %d %s
% % Computer : n160.star.cs.uiowa.edu
% % Model    : x86_64 x86_64
% % CPU      : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% % Memory   : 32286.75MB
% % OS       : Linux 2.6.32-431.11.2.el6.x86_64
% % CPULimit : 300
% % DateTime : Thu Jun  5 13:47:18 CDT 2014
% % CPUTime  : 83.25 
% ============================== Prover9 ===============================
% Prover9 (32) version 2009-11A, November 2009.
% Process 30401 was started by sandbox on n160.star.cs.uiowa.edu,
% Thu Jun  5 13:47:18 2014
% The command was "./prover9 -t 300 -f /tmp/Prover9_30369_n160.star.cs.uiowa.edu".
% ============================== end of head ===========================
% 
% ============================== INPUT =================================
% 
% % Reading from file /tmp/Prover9_30369_n160.star.cs.uiowa.edu
% 
% set(prolog_style_variables).
% set(auto2).
% % set(auto2) -> set(auto).
% % set(auto) -> set(auto_inference).
% % set(auto) -> set(auto_setup).
% % set(auto_setup) -> set(predicate_elim).
% % set(auto_setup) -> assign(eq_defs, unfold).
% % set(auto) -> set(auto_limits).
% % set(auto_limits) -> assign(max_weight, "100.000").
% % set(auto_limits) -> assign(sos_limit, 20000).
% % set(auto) -> set(auto_denials).
% % set(auto) -> set(auto_process).
% % set(auto2) -> assign(new_constants, 1).
% % set(auto2) -> assign(fold_denial_max, 3).
% % set(auto2) -> assign(max_weight, "200.000").
% % set(auto2) -> assign(max_hours, 1).
% % assign(max_hours, 1) -> assign(max_seconds, 3600).
% % set(auto2) -> assign(max_seconds, 0).
% % set(auto2) -> assign(max_minutes, 5).
% % assign(max_minutes, 5) -> assign(max_seconds, 300).
% % set(auto2) -> set(sort_initial_sos).
% % set(auto2) -> assign(sos_limit, -1).
% % set(auto2) -> assign(lrs_ticks, 3000).
% % set(auto2) -> assign(max_megs, 400).
% % set(auto2) -> assign(stats, some).
% % set(auto2) -> clear(echo_input).
% % set(auto2) -> set(quiet).
% % set(auto2) -> clear(print_initial_clauses).
% % set(auto2) -> clear(print_given).
% assign(lrs_ticks,-1).
% assign(sos_limit,10000).
% assign(order,kbo).
% set(lex_order_vars).
% clear(print_given).
% 
% % formulas(sos).  % not echoed (17 formulas)
% 
% ============================== end of input ==========================
% 
% % From the command line: assign(max_seconds, 300).
% 
% ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 
% % Formulas that are not ordinary clauses:
% 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause).  [assumption].
% 2 (all C all B all A addition(A,addition(B,C)) = addition(addition(A,B),C)) # label(additive_associativity) # label(axiom) # label(non_clause).  [assumption].
% 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause).  [assumption].
% 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause).  [assumption].
% 5 (all A all B all C multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C)) # label(multiplicative_associativity) # label(axiom) # label(non_clause).  [assumption].
% 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause).  [assumption].
% 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause).  [assumption].
% 8 (all A all B all C multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C))) # label(right_distributivity) # label(axiom) # label(non_clause).  [assumption].
% 9 (all A all B all C multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C))) # label(left_distributivity) # label(axiom) # label(non_clause).  [assumption].
% 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause).  [assumption].
% 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause).  [assumption].
% 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause).  [assumption].
% 13 (all X0 (test(X0) <-> (exists X1 complement(X1,X0)))) # label(test_1) # label(axiom) # label(non_clause).  [assumption].
% 14 (all X0 all X1 (complement(X1,X0) <-> multiplication(X0,X1) = zero & multiplication(X1,X0) = zero & addition(X0,X1) = one)) # label(test_2) # label(axiom) # label(non_clause).  [assumption].
% 15 (all X0 all X1 (test(X0) -> (c(X0) = X1 <-> complement(X0,X1)))) # label(test_3) # label(axiom) # label(non_clause).  [assumption].
% 16 (all X0 (-test(X0) -> c(X0) = zero)) # label(test_4) # label(axiom) # label(non_clause).  [assumption].
% 17 -(all X0 all X1 (test(X1) & test(X0) -> one = addition(addition(multiplication(addition(X1,c(X1)),X0),multiplication(addition(X0,c(X0)),X1)),multiplication(c(X0),c(X1))))) # label(goals) # label(negated_conjecture) # label(non_clause).  [assumption].
% 
% ============================== end of process non-clausal formulas ===
% 
% ============================== PROCESS INITIAL CLAUSES ===============
% 
% ============================== PREDICATE ELIMINATION =================
% 18 -test(A) | complement(f1(A),A) # label(test_1) # label(axiom).  [clausify(13)].
% 19 test(c2) # label(goals) # label(negated_conjecture).  [clausify(17)].
% 20 test(c1) # label(goals) # label(negated_conjecture).  [clausify(17)].
% 21 test(A) | c(A) = zero # label(test_4) # label(axiom).  [clausify(16)].
% 22 test(A) | -complement(B,A) # label(test_1) # label(axiom).  [clausify(13)].
% Derived: complement(f1(c2),c2).  [resolve(18,a,19,a)].
% Derived: complement(f1(c1),c1).  [resolve(18,a,20,a)].
% Derived: complement(f1(A),A) | c(A) = zero.  [resolve(18,a,21,a)].
% Derived: complement(f1(A),A) | -complement(B,A).  [resolve(18,a,22,a)].
% 23 -test(A) | c(A) != B | complement(A,B) # label(test_3) # label(axiom).  [clausify(15)].
% Derived: c(c2) != A | complement(c2,A).  [resolve(23,a,19,a)].
% Derived: c(c1) != A | complement(c1,A).  [resolve(23,a,20,a)].
% Derived: c(A) != B | complement(A,B) | c(A) = zero.  [resolve(23,a,21,a)].
% Derived: c(A) != B | complement(A,B) | -complement(C,A).  [resolve(23,a,22,a)].
% 24 -test(A) | c(A) = B | -complement(A,B) # label(test_3) # label(axiom).  [clausify(15)].
% Derived: c(c2) = A | -complement(c2,A).  [resolve(24,a,19,a)].
% Derived: c(c1) = A | -complement(c1,A).  [resolve(24,a,20,a)].
% Derived: c(A) = B | -complement(A,B) | c(A) = zero.  [resolve(24,a,21,a)].
% Derived: c(A) = B | -complement(A,B) | -complement(C,A).  [resolve(24,a,22,a)].
% 25 leq(A,B) | addition(A,B) != B # label(order) # label(axiom).  [clausify(12)].
% 26 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom).  [clausify(12)].
% 
% ============================== end predicate elimination =============
% 
% Auto_denials:  (non-Horn, no changes).
% 
% Term ordering decisions:
% Function symbol KB weights:  zero=1. one=1. c1=1. c2=1. multiplication=1. addition=1. c=1. f1=1.
% 
% ============================== end of process initial clauses ========
% 
% ============================== CLAUSES FOR SEARCH ====================
% 
% ============================== end of clauses for search =============
% 
% ============================== SEARCH ================================
% 
% % Starting search at 0.01 seconds.
% 
% Low Water (keep): wt=82.000, iters=3367
% 
% Low Water (keep): wt=74.000, iters=3466
% 
% Low Water (keep): wt=68.000, iters=3436
% 
% Low Water (keep): wt=67.000, iters=3381
% 
% Low Water (keep): wt=64.000, iters=3361
% 
% Low Water (keep): wt=60.000, iters=3424
% 
% Low Water (keep): wt=58.000, iters=3366
% 
% Low Water (keep): wt=54.000, iters=3485
% 
% Low Water (keep): wt=53.000, iters=3420
% 
% Low Water (keep): wt=52.000, iters=3417
% 
% Low Water (keep): wt=48.000, iters=3350
% 
% Low Water (keep): wt=46.000, iters=3339
% 
% Low Water (keep): wt=44.000, iters=3340
% 
% Low Water (keep): wt=42.000, iters=3343
% 
% Low Water (keep): wt=40.000, iters=3346
% 
% Low Water (keep): wt=39.000, iters=3362
% 
% Low Water (keep): wt=37.000, iters=3342
% 
% Low Water (keep): wt=36.000, iters=3393
% 
% Low Water (keep): wt=35.000, iters=3384
% 
% Low Water (keep): wt=34.000, iters=3343
% 
% Low Water (keep): wt=33.000, iters=3360
% 
% Low Water (keep): wt=32.000, iters=3342
% 
% Low Water (keep): wt=31.000, iters=3360
% 
% NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 105 (0.00 of 2.02 sec).
% 
% Low Water (keep): wt=30.000, iters=3407
% 
% Low Water (keep): wt=29.000, iters=3390
% 
% Low Water (keep): wt=28.000, iters=3360
% 
% Low Water (keep): wt=27.000, iters=3466
% 
% Low Water (keep): wt=26.000, iters=3336
% 
% Low Water (keep): wt=25.000, iters=3364
% 
% Low Water (keep): wt=24.000, iters=3338
% 
% Low Water (displace): id=5784, wt=107.000
% 
% Low Water (displace): id=5800, wt=88.000
% 
% Low Water (displace): id=5461, wt=85.000
% 
% Low Water (displace): id=5801, wt=82.000
% 
% Low Water (displace): id=5042, wt=81.000
% 
% Low Water (displace): id=5795, wt=80.000
% 
% Low Water (displace): id=5044, wt=79.000
% 
% Low Water (displace): id=5420, wt=75.000
% 
% Low Water (displace): id=6087, wt=74.000
% 
% Low Water (displace): id=5799, wt=72.000
% 
% Low Water (displace): id=6138, wt=68.000
% 
% Low Water (displace): id=6119, wt=67.000
% 
% Low Water (displace): id=5532, wt=66.000
% 
% Low Water (displace): id=6174, wt=64.000
% 
% Low Water (displace): id=11681, wt=21.000
% 
% Low Water (displace): id=11688, wt=18.000
% 
% Low Water (keep): wt=23.000, iters=3342
% 
% Low Water (displace): id=11808, wt=17.000
% 
% Low Water (displace): id=11848, wt=16.000
% 
% Low Water (displace): id=11862, wt=15.000
% 
% Low Water (displace): id=11894, wt=14.000
% 
% Low Water (displace): id=13098, wt=13.000
% 
% Low Water (keep): wt=22.000, iters=3333
% 
% Low Water (keep): wt=21.000, iters=3333
% 
% Low Water (keep): wt=20.000, iters=3338
% 
% Low Water (keep): wt=19.000, iters=3333
% 
% Low Water (keep): wt=18.000, iters=3345
% 
% Low Water (keep): wt=17.000, iters=3351
% 
% Low Water (keep): wt=16.000, iters=3333
% 
% ============================== PROOF =================================
% % SZS status Theorem
% % SZS output start Refutation
% 
% % Proof 1 at 82.10 (+ 1.03) seconds.
% % Length of proof is 107.
% % Level of proof is 14.
% % Maximum clause weight is 21.000.
% % Given clauses 3936.
% 
% 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause).  [assumption].
% 2 (all C all B all A addition(A,addition(B,C)) = addition(addition(A,B),C)) # label(additive_associativity) # label(axiom) # label(non_clause).  [assumption].
% 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause).  [assumption].
% 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause).  [assumption].
% 5 (all A all B all C multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C)) # label(multiplicative_associativity) # label(axiom) # label(non_clause).  [assumption].
% 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause).  [assumption].
% 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause).  [assumption].
% 8 (all A all B all C multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C))) # label(right_distributivity) # label(axiom) # label(non_clause).  [assumption].
% 9 (all A all B all C multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C))) # label(left_distributivity) # label(axiom) # label(non_clause).  [assumption].
% 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause).  [assumption].
% 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause).  [assumption].
% 13 (all X0 (test(X0) <-> (exists X1 complement(X1,X0)))) # label(test_1) # label(axiom) # label(non_clause).  [assumption].
% 14 (all X0 all X1 (complement(X1,X0) <-> multiplication(X0,X1) = zero & multiplication(X1,X0) = zero & addition(X0,X1) = one)) # label(test_2) # label(axiom) # label(non_clause).  [assumption].
% 15 (all X0 all X1 (test(X0) -> (c(X0) = X1 <-> complement(X0,X1)))) # label(test_3) # label(axiom) # label(non_clause).  [assumption].
% 17 -(all X0 all X1 (test(X1) & test(X0) -> one = addition(addition(multiplication(addition(X1,c(X1)),X0),multiplication(addition(X0,c(X0)),X1)),multiplication(c(X0),c(X1))))) # label(goals) # label(negated_conjecture) # label(non_clause).  [assumption].
% 18 -test(A) | complement(f1(A),A) # label(test_1) # label(axiom).  [clausify(13)].
% 19 test(c2) # label(goals) # label(negated_conjecture).  [clausify(17)].
% 20 test(c1) # label(goals) # label(negated_conjecture).  [clausify(17)].
% 22 test(A) | -complement(B,A) # label(test_1) # label(axiom).  [clausify(13)].
% 23 -test(A) | c(A) != B | complement(A,B) # label(test_3) # label(axiom).  [clausify(15)].
% 24 -test(A) | c(A) = B | -complement(A,B) # label(test_3) # label(axiom).  [clausify(15)].
% 27 addition(A,zero) = A # label(additive_identity) # label(axiom).  [clausify(3)].
% 28 addition(A,A) = A # label(additive_idempotence) # label(axiom).  [clausify(4)].
% 29 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom).  [clausify(6)].
% 30 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom).  [clausify(7)].
% 31 multiplication(A,zero) = zero # label(right_annihilation) # label(axiom).  [clausify(10)].
% 32 multiplication(zero,A) = zero # label(left_annihilation) # label(axiom).  [clausify(11)].
% 33 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom).  [clausify(1)].
% 34 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom).  [clausify(2)].
% 35 addition(A,addition(B,C)) = addition(C,addition(A,B)).  [copy(34),rewrite([33(2)]),flip(a)].
% 36 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom).  [clausify(5)].
% 37 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom).  [clausify(8)].
% 38 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)).  [copy(37),flip(a)].
% 39 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(left_distributivity) # label(axiom).  [clausify(9)].
% 40 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B).  [copy(39),flip(a)].
% 41 addition(addition(multiplication(addition(c2,c(c2)),c1),multiplication(addition(c1,c(c1)),c2)),multiplication(c(c1),c(c2))) != one # label(goals) # label(negated_conjecture).  [clausify(17)].
% 42 addition(multiplication(c(c1),c(c2)),addition(multiplication(addition(c1,c(c1)),c2),multiplication(addition(c2,c(c2)),c1))) != one.  [copy(41),rewrite([33(13),33(19)])].
% 44 -complement(A,B) | multiplication(A,B) = zero # label(test_2) # label(axiom).  [clausify(14)].
% 45 -complement(A,B) | addition(B,A) = one # label(test_2) # label(axiom).  [clausify(14)].
% 46 -complement(A,B) | addition(A,B) = one.  [copy(45),rewrite([33(2)])].
% 47 complement(A,B) | multiplication(B,A) != zero | multiplication(A,B) != zero | addition(B,A) != one # label(test_2) # label(axiom).  [clausify(14)].
% 48 complement(A,B) | multiplication(B,A) != zero | multiplication(A,B) != zero | addition(A,B) != one.  [copy(47),rewrite([33(8)])].
% 49 complement(f1(c2),c2).  [resolve(18,a,19,a)].
% 50 complement(f1(c1),c1).  [resolve(18,a,20,a)].
% 52 complement(f1(A),A) | -complement(B,A).  [resolve(18,a,22,a)].
% 53 c(c2) != A | complement(c2,A).  [resolve(23,a,19,a)].
% 54 c(c1) != A | complement(c1,A).  [resolve(23,a,20,a)].
% 60 c(A) = B | -complement(A,B) | -complement(C,A).  [resolve(24,a,22,a)].
% 64 addition(A,addition(A,B)) = addition(A,B).  [para(35(a,1),28(a,1)),rewrite([33(1),33(2),35(2,R),28(1),33(3)])].
% 65 addition(zero,multiplication(A,B)) = multiplication(A,B).  [para(27(a,1),38(a,2,2)),rewrite([31(3),33(3)])].
% 66 multiplication(A,addition(B,one)) = addition(A,multiplication(A,B)).  [para(29(a,1),38(a,1,1)),rewrite([33(4)]),flip(a)].
% 67 multiplication(addition(A,one),B) = addition(B,multiplication(A,B)).  [para(30(a,1),40(a,1,1)),rewrite([33(4)]),flip(a)].
% 68 addition(multiplication(A,multiplication(B,C)),multiplication(D,C)) = multiplication(addition(D,multiplication(A,B)),C).  [para(36(a,1),40(a,1,1)),rewrite([33(6)])].
% 72 complement(one,zero).  [resolve(48,d,27,a),rewrite([29(6),31(9)]),xx(b),xx(c)].
% 77 addition(c2,f1(c2)) = one.  [resolve(49,a,46,a),rewrite([33(4)])].
% 80 addition(c1,f1(c1)) = one.  [resolve(50,a,46,a),rewrite([33(4)])].
% 86 complement(c2,c(c2)).  [resolve(53,a,30,a(flip)),rewrite([30(5)])].
% 88 complement(c1,c(c1)).  [resolve(54,a,30,a(flip)),rewrite([30(5)])].
% 101 c(zero) = A | -complement(zero,A).  [resolve(72,a,60,c)].
% 104 addition(zero,one) = one.  [resolve(72,a,46,a),rewrite([33(3)])].
% 108 addition(c2,c(c2)) = one.  [resolve(86,a,46,a)].
% 109 multiplication(c2,c(c2)) = zero.  [resolve(86,a,44,a)].
% 112 addition(c1,addition(multiplication(c(c1),c(c2)),multiplication(addition(c1,c(c1)),c2))) != one.  [back_rewrite(42),rewrite([108(15),30(14),33(13),35(14,R),33(13)])].
% 115 complement(f1(c(c1)),c(c1)).  [resolve(88,a,52,b)].
% 116 addition(c1,c(c1)) = one.  [resolve(88,a,46,a)].
% 119 addition(c1,addition(c2,multiplication(c(c1),c(c2)))) != one.  [back_rewrite(112),rewrite([116(10),30(9),33(8)])].
% 127 complement(zero,one).  [resolve(104,a,48,d),rewrite([31(6),29(9)]),xx(b),xx(c)].
% 138 addition(A,multiplication(B,addition(C,one))) = addition(B,addition(A,multiplication(B,C))).  [para(66(a,2),35(a,2,2)),rewrite([33(2)]),flip(a)].
% 166 addition(one,c2) = one.  [para(77(a,1),64(a,1,2)),rewrite([33(3),77(7)])].
% 175 addition(A,multiplication(A,c2)) = A.  [para(166(a,1),38(a,2,2)),rewrite([29(2),29(5)])].
% 176 addition(A,multiplication(c2,A)) = A.  [para(166(a,1),40(a,2,1)),rewrite([30(2),30(5)])].
% 190 addition(one,c1) = one.  [para(80(a,1),64(a,1,2)),rewrite([33(3),80(7)])].
% 239 multiplication(c2,addition(A,c(c2))) = multiplication(c2,A).  [para(109(a,1),38(a,1,1)),rewrite([65(4),33(6)]),flip(a)].
% 240 multiplication(addition(A,c2),c(c2)) = multiplication(A,c(c2)).  [para(109(a,1),40(a,1,1)),rewrite([65(5),33(5)]),flip(a)].
% 243 multiplication(addition(c2,multiplication(A,B)),c(c2)) = multiplication(A,multiplication(B,c(c2))).  [para(109(a,1),68(a,1,2)),rewrite([33(6),65(6)]),flip(a)].
% 259 addition(c(c1),f1(c(c1))) = one.  [resolve(115,a,46,a),rewrite([33(6)])].
% 328 c(zero) = one.  [resolve(101,b,127,a)].
% 330 one = A | -complement(zero,A).  [back_rewrite(101),rewrite([328(2)])].
% 333 -complement(zero,addition(c1,addition(c2,multiplication(c(c1),c(c2))))).  [ur(330,a,119,a(flip))].
% 341 addition(zero,addition(c1,addition(c2,multiplication(c(c1),c(c2))))) != one.  [ur(48,a,333,a,b,31,a,c,32,a)].
% 343 -complement(zero,addition(zero,addition(c1,addition(c2,multiplication(c(c1),c(c2)))))).  [ur(330,a,341,a(flip))].
% 344 addition(A,addition(B,multiplication(A,c2))) = addition(A,B).  [para(175(a,1),35(a,2,2)),rewrite([33(3),33(5)])].
% 347 addition(A,addition(B,multiplication(c2,A))) = addition(A,B).  [para(176(a,1),35(a,2,2)),rewrite([33(3),33(5)])].
% 400 addition(one,c(c1)) = one.  [para(259(a,1),64(a,1,2)),rewrite([33(4),259(10)])].
% 409 addition(A,multiplication(c(c1),A)) = A.  [para(400(a,1),40(a,2,1)),rewrite([30(2),30(6)])].
% 496 addition(A,addition(B,multiplication(c(c1),A))) = addition(A,B).  [para(409(a,1),35(a,2,2)),rewrite([33(4),33(6)])].
% 578 multiplication(c2,c2) = c2.  [para(108(a,1),239(a,1,2)),rewrite([29(3)]),flip(a)].
% 583 multiplication(c2,multiplication(c2,A)) = multiplication(c2,A).  [para(578(a,1),36(a,1,1)),flip(a)].
% 584 multiplication(c2,addition(A,c2)) = multiplication(c2,addition(A,one)).  [para(578(a,1),38(a,1,1)),rewrite([66(4,R),33(7)]),flip(a)].
% 585 multiplication(addition(A,c2),c2) = multiplication(addition(A,one),c2).  [para(578(a,1),40(a,1,1)),rewrite([67(4,R),33(6)]),flip(a)].
% 638 multiplication(c2,addition(A,multiplication(c2,B))) = multiplication(c2,addition(B,A)).  [para(583(a,1),38(a,1,1)),rewrite([38(5),33(7)]),flip(a)].
% 1008 addition(multiplication(A,c(c2)),multiplication(addition(A,c2),B)) = multiplication(addition(A,c2),addition(B,c(c2))).  [para(240(a,1),38(a,1,1)),rewrite([33(12)])].
% 1127 addition(A,multiplication(addition(A,B),c2)) = addition(A,multiplication(B,c2)).  [para(40(a,1),344(a,1,2)),rewrite([33(1)])].
% 1133 addition(one,addition(c2,c(c1))) = one.  [para(400(a,1),344(a,2)),rewrite([30(6),33(5)])].
% 7790 addition(c1,multiplication(c(c1),c2)) = addition(c1,c2).  [para(116(a,1),1127(a,1,2,1)),rewrite([30(4)]),flip(a)].
% 7795 addition(one,multiplication(c(c1),c2)) = one.  [para(400(a,1),1127(a,1,2,1)),rewrite([30(4),166(3)]),flip(a)].
% 7866 addition(A,multiplication(c(c1),multiplication(c2,A))) = A.  [para(7795(a,1),40(a,2,1)),rewrite([30(2),36(5),30(8)])].
% 7957 multiplication(c2,addition(multiplication(c2,c1),multiplication(c(c1),c2))) = c2.  [para(7790(a,1),638(a,2,2)),rewrite([33(9),584(15),33(14),190(14),29(13)])].
% 8017 multiplication(c(c1),addition(one,multiplication(c2,c(c1)))) = c(c1).  [para(7866(a,1),66(a,2)),rewrite([33(8)])].
% 8275 addition(multiplication(c2,c1),multiplication(c(c1),c2)) = c2.  [para(7957(a,1),67(a,2,2)),rewrite([33(3),166(3),30(10),33(18),496(18),66(13,R),33(12),190(12),29(11)])].
% 8278 addition(c(c1),multiplication(c2,c1)) = addition(c2,c(c1)).  [para(8275(a,1),138(a,2,2)),rewrite([33(8),166(8),29(7),33(6),33(10)])].
% 8348 addition(c1,addition(c2,c(c1))) = one.  [para(8278(a,1),347(a,1,2)),rewrite([116(10)])].
% 8374 addition(one,multiplication(c2,c(c1))) = one.  [para(8017(a,1),67(a,2,2)),rewrite([33(4),400(4),30(8),33(15),347(15),33(10),400(10)])].
% 8375 multiplication(addition(c2,c(c1)),c(c2)) = multiplication(c(c1),c(c2)).  [para(8017(a,1),243(a,1,1,2)),rewrite([8374(15),30(13)])].
% 23294 addition(multiplication(A,c(c2)),multiplication(addition(A,one),c2)) = addition(A,c2).  [para(108(a,1),1008(a,2,2)),rewrite([585(7),29(12)])].
% 27824 addition(c2,multiplication(c(c1),c(c2))) = addition(c2,c(c1)).  [para(8375(a,1),23294(a,1,1)),rewrite([33(11),1133(11),30(8),33(7),33(13),64(13)])].
% 27825 $F.  [back_rewrite(343),rewrite([27824(10),8348(8),104(4)]),unit_del(a,127)].
% 
% % SZS output end Refutation
% ============================== end of proof ==========================
% 
% ============================== STATISTICS ============================
% 
% Given=3936. Generated=2634923. Kept=27792. proofs=1.
% Usable=3693. Sos=9980. Demods=1678. Limbo=1, Disabled=14155. Hints=0.
% Megabytes=21.49.
% User_CPU=82.10, System_CPU=1.03, Wall_clock=83.
% 
% ============================== end of statistics =====================
% 
% ============================== end of search =========================
% 
% THEOREM PROVED
% % SZS status Theorem
% 
% Exiting with 1 proof.
% 
% Process 30401 exit (max_proofs) Thu Jun  5 13:48:41 2014
% Prover9 interrupted
% 
% EOF
%------------------------------------------------------------------------------